https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-mean/v/what-is-geometric-mean 2025-03-24T05:52:22.847271672Z GM क्या है? (What is GM?) We know about Arithmetic mean. In this video, we'll also learn about Geometric mean. Both of them are more alike than they look. Let's find out more! We first define the means. We try to find the values of AM and GM for two simple sequences. We then generalise our results to get the formula for both AM and GM. Finally, we tackle a practice problem to strengthen this concept. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw GM क्या है? (What is GM?) We know about Arithmetic mean. In this video, we'll also learn about Geometric mean. Both of them are more alike than they look. Let's find out more! We first define the means. We try to find the values of AM and GM for two simple sequences. We then generalise our results to get the formula for both AM and GM. Finally, we tackle a practice problem to strengthen this concept. https://cdn.kastatic.org/ka-youtube-converted/kExp6yr5-7I.mp4/kExp6yr5-7I.mp4 534 गुणोत्तर माध्य (Geometric mean) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-mean/v/relationship-between-am-and-gm 2025-03-24T05:52:22.847271672Z AM तथा GM के बीच संबंध (Relationship between AM and GM) What is the relationship between AM and GM? Which one is greater than the other? Let's find out. We first tackle a concrete example where we realise that AM is greater. We then break down a rigorous proof showing that that's almost always the case. Finally, we zoom in on the corner case where both AM and GM are equal. We realise that the numbers themselves have to be equal for this to happen! Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw AM तथा GM के बीच संबंध (Relationship between AM and GM) What is the relationship between AM and GM? Which one is greater than the other? Let's find out. We first tackle a concrete example where we realise that AM is greater. We then break down a rigorous proof showing that that's almost always the case. Finally, we zoom in on the corner case where both AM and GM are equal. We realise that the numbers themselves have to be equal for this to happen! https://cdn.kastatic.org/ka-youtube-converted/wEMS7X6aHZs.mp4/wEMS7X6aHZs.mp4 264 गुणोत्तर माध्य (Geometric mean) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-mean/v/finding-n-to-get-the-gm-of-a-and-b 2025-03-24T05:52:22.847271672Z a और b का गुणोत्तर माध्य ज्ञात करने के लिए n ढूँढना (Finding n to get the GM of a and b) Find the value of n such that something super hairy becomes the GM of a and b. Let's get our hands dirty and tackle this one! Although this problem is typically categorised as a GM problem, the only place where we need the GM formula is the first step. After that, we leverage a number of prerequisites from linear equations, exponents, roots of a solution, etc. This is what truly makes this problem challenging. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw a और b का गुणोत्तर माध्य ज्ञात करने के लिए n ढूँढना (Finding n to get the GM of a and b) Find the value of n such that something super hairy becomes the GM of a and b. Let's get our hands dirty and tackle this one! Although this problem is typically categorised as a GM problem, the only place where we need the GM formula is the first step. After that, we leverage a number of prerequisites from linear equations, exponents, roots of a solution, etc. This is what truly makes this problem challenging. https://cdn.kastatic.org/ka-youtube-converted/WX-vfWF5hSA.mp4/WX-vfWF5hSA.mp4 503 गुणोत्तर माध्य (Geometric mean) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-mean/v/proving-that-ratio-of-two-terms-is-a-given-irrational-number 2025-03-24T05:52:22.847271672Z सिद्ध करना कि दो पदों का अनुपात दी गयी अपरिमेय संख्या है (Proving that ratio of two terms is a given irrational number) Given a clue about two numbers and their GM, prove that their ratio is a given irrational number. Another hairy problem. Although this problem is typically categorised as a GM problem, the only place where we need the GM formula is the first step. After that, we leverage a number of prerequisites from linear equations, quadratic equations, rationalisation, etc. This is what truly makes this problem challenging. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw सिद्ध करना कि दो पदों का अनुपात दी गयी अपरिमेय संख्या है (Proving that ratio of two terms is a given irrational number) Given a clue about two numbers and their GM, prove that their ratio is a given irrational number. Another hairy problem. Although this problem is typically categorised as a GM problem, the only place where we need the GM formula is the first step. After that, we leverage a number of prerequisites from linear equations, quadratic equations, rationalisation, etc. This is what truly makes this problem challenging. https://cdn.kastatic.org/ka-youtube-converted/I-XshM6ih7A.mp4/I-XshM6ih7A.mp4 375 गुणोत्तर माध्य (Geometric mean) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-mean/v/given-am-gm-finding-numbers-proof 2025-03-24T05:52:22.847271672Z दिए गए AM एवं GM के लिए संख्याएँ ज्ञात करना (उपपत्ति पर आधारित) (Given AM GM - Finding numbers (proof)) Given AM and GM, can we find the numbers? Let's learn how to move in the reverse direction. In this video, we approach this problem through the world of quadratic equations. Since AM deals with sum of roots and GM deals with product of roots, we leverage both of these to generate a quadratic equation. The roots of this equation, turns out, are the numbers we're looking for! Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw दिए गए AM एवं GM के लिए संख्याएँ ज्ञात करना (उपपत्ति पर आधारित) (Given AM GM - Finding numbers (proof)) Given AM and GM, can we find the numbers? Let's learn how to move in the reverse direction. In this video, we approach this problem through the world of quadratic equations. Since AM deals with sum of roots and GM deals with product of roots, we leverage both of these to generate a quadratic equation. The roots of this equation, turns out, are the numbers we're looking for! https://cdn.kastatic.org/ka-youtube-converted/mj3548PhpGY.mp4/mj3548PhpGY.mp4 164 गुणोत्तर माध्य (Geometric mean) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-mean/v/given-am-and-gm-finding-numbers 2025-03-24T05:52:22.847271672Z दिए गए AM और GM के लिए संख्याएँ ज्ञात करना (Given AM and GM - finding numbers) Given AM and GM, can we find the numbers? Let's learn how to move in the reverse direction. In this video, we approach this problem through the world of quadratic equations. Since AM deals with sum of roots and GM deals with product of roots, we leverage both of these to generate a quadratic equation. The roots of this equation, turns out, are the numbers we're looking for! Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw दिए गए AM और GM के लिए संख्याएँ ज्ञात करना (Given AM and GM - finding numbers) Given AM and GM, can we find the numbers? Let's learn how to move in the reverse direction. In this video, we approach this problem through the world of quadratic equations. Since AM deals with sum of roots and GM deals with product of roots, we leverage both of these to generate a quadratic equation. The roots of this equation, turns out, are the numbers we're looking for! https://cdn.kastatic.org/ka-youtube-converted/7mzhFFD_StE.mp4/7mzhFFD_StE.mp4 216 गुणोत्तर माध्य (Geometric mean)